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Simplifying x2 + x = 400 Reorder the terms: x + x2 = 400 Solving x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + x + x2 = 0 + 400 x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 x + x2 = 400 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 400 + 0.25 Reorder the terms: 0.25 + x + x2 = 400 + 0.25 Combine like terms: 400 + 0.25 = 400.25 0.25 + x + x2 = 400.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (x + 0.5) equal to 20.006249024 and -20.006249024.Subproblem 1
x + 0.5 = 20.006249024 Simplifying x + 0.5 = 20.006249024 Reorder the terms: 0.5 + x = 20.006249024 Solving 0.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 20.006249024 + -0.5 x = 20.006249024 + -0.5 Combine like terms: 20.006249024 + -0.5 = 19.506249024 x = 19.506249024 Simplifying x = 19.506249024Subproblem 2
x + 0.5 = -20.006249024 Simplifying x + 0.5 = -20.006249024 Reorder the terms: 0.5 + x = -20.006249024 Solving 0.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -20.006249024 + -0.5 x = -20.006249024 + -0.5 Combine like terms: -20.006249024 + -0.5 = -20.506249024 x = -20.506249024 Simplifying x = -20.506249024Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.506249024, -20.506249024}
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